A Graph Vertex-Coloring-Based Parallel Block Coordinate Descent Method for Solving the Traffic Assignment Problem

Abstract

Traffic assignment is an essential component of the traditional four-step transportation planning methodology and significantly contributes to the prediction of traffic flow distribution and optimization of traffic planning. Existing algorithms for solving the user equilibrium traffic assignment problem typically rely on equal intervals and random sampling strategies to divide a set of origin-destination (OD) pairs. However, these sampling strategies fail to address the path overlap issue among OD pairs and often depend on sensitivity analyses to partition the OD set, hindering the efficiency of task parallelism. To address this challenge, the OD grouping problem was formulated as a vertex-coloring problem, which was translated into an integer linear programming (ILP) model. The largest degree first algorithm was proposed to solve the ILP problem, enabling the identification of OD pairs within each block with minimal path overlap. Thereafter, the results of the OD grouping based on vertex coloring were incorporated into the parallel block coordinate descent (PBCD) method, increasing the number of OD subproblems within each block and enhancing the parallel computation. An adaptive algorithm is further proposed to address the OD-based restricted subproblem depending on the number of paths for a given OD pair. The proposed method is evaluated based on various large-scale transportation networks and compared with existing algorithms, demonstrating its effectiveness in reducing path overlap within blocks and improving the efficiency of solving traffic assignment problems in large-scale networks.

Keywords: Traffic Assignment, Vertex-coloring, Integer Linear Programming, Parallel Block Coordinate Descent Method